Nonlinear Coherent Structures in Physics and Biology

476 Pages·1994·19.98 MB·English

by  J. C. Eilbeck

Nonlinear Coherent Structures
in Physics and Biology
NATO ASI Series
Advanced Science Institutes Series
A series presenting the results of activities sponsored by the NA TO Science
Committee, which aims at the dissemination of advanced scientific and technological
knowledge, with a view to strengthening links between scientific communities.
The series is published by an international board of publishers in conjunction
with the NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics New York and London
C Mathematical and Physical Sciences Kluwer Academic Publishers
D Behavioral and Social Sciences Dordrecht, Boston, and London
E Applied Sciences
F Computer and Systems Sciences Springer-Verlag
G Ecological Sciences Berlin, Heidelberg, New York, London,
H Cell Biology Paris, Tokyo, Hong Kong, and Barcelona
I Global Environmental Change
Recent Volumes in this Series
Volume 328 -Quantum Field Theory and String Theory
edited by Laurent Baulieu, Vladimir Dotsenko, Vladimir Kazakov,
and Paul Windey
Volume 329 -Nonlinear Coherent Structures in PhYSics and Biology
edited by K. H. Spatschek and F. G. Mertens
Volume 330 -Coherent Optical Interactions in Semiconductors
edited by R. T. Phillips
Volume 331 -Hamiltonian Mechanics: Integrability and Chaotic Behavior
edited by John Seimenis
Volume 332 -Deterministic Chaos in General Relativity
edited by David Hobill, Adrian Burd, and Alan Coley
Volume 333 - Perspectives in the Structure of Hadronic Systems
edited by M. N. Harakeh, J. H. Koch, and O. Scholten
Volume 334 -Frontier Topics in Nuclear Physics
edited by Werner Scheid and Aurel Sandulescu
Volume 335 - Hot and Dense Nuclear Matter
edited by Walter Greiner, Horst Stocker, and Andre Gallmann
~
Series B: Physics
Nonlinear Coherent Structures
in Physics and Biology
Edited by
K. H. Spatschek
Heinrich-Heine University, Dusseldorf
Dusseldorf, Germay
and
F. G. Mertens
University of Bayreuth
Bayreuth, Germany
Springer Science+Business Media, LLC
Proceedings of a NATO Advanced Research Workshop on
Nonlinear Coherent Structures in Physics and Biology,
held June 1-4, 1993,
in Bayreuth, Germany
NATO-PCO-DATA BASE
The electronic index to the NATO ASI Series provides full bibliographical references (with
keywords and/or abstracts) to more than 30,000 contributions from international scientists
published in all sections of the NATO ASI Series. Access to the NATO-PCO-DATA BASE is
possible in two ways:
—via online FILE 128 (NATO-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei,
I-00044 Frascati, Italy
—via CD-ROM "NATO Science and Technology Disk" with user-friendly retrieval software in
English, French, and German (©WTV GmbH and DATAWARE Technologies, Inc. 1989). The
CD-ROM also contains the AGARD Aerospace Database.
The CD-ROM can be ordered through any member of the Board of Publishers or through
NATO-PCO, Overijse, Belgium.
Library of Congress Cataloging-1n-Publication Data
Nonlinear coherent structures in physics and biology / edited by K.H.
Spatschek and F.G. Mertens.
p. cm. ~ (NATO ASI series. Series B, Physics ; v. 329)
"Published in cooperation with NATO Scientific Affairs Division."
"Proceedings of a NATO Advanced Research Workshop on Nonlinear
Coherent Structures 1n Physics and Biology, held June 1-4, 1993, in
Bayreuth, Germany"—T.p. verso.
Includes bibliographical references and index.
1. Solitons—Congresses. 2. Nonlinear theories—Congresses.
3. Lattice theory—Congresses. 4. Biophysics—Congresses.
I. Spatschek, Karl-Heinz. II. Mertens, Franz-Georg. III. North
Atlantic Treaty Organization. Scientific Affairs Division.
IV. NATO Advanced Research Workshop on Nonlinear Coherent Structures
in Physics and Biology (8th 1993 ; Bayreuth, Germany) V. Series.
:
QC174.26.W28N65 1994
530.1' 4—dc20 94-35396
CtP
ISBN 978-1-4899-1345-6 ISBN 978-1-4899-1343-2 (eBook)
DOI 10.1007/978-1-4899-1343-2
© Springer Science+Business Media New York 1994
Originally published by Plenum Press, New York in 1994
Softcover reprint of the hardcover 1st edition 1994
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in any
form or by any means, electronic, mechanical, photocopying, microfilming, recording, or
otherwise, without written permission from the Publisher
SPECIAL PROGRAM ON CHAOS, ORDER, AND PATTERNS
This book contains the proceedings of a NATO Advanced Research Workshop held
within the program of activities of the NATO Special Program on Chaos, Order, and
Patterns.
Volume 208 - MEASURES OF COMPLEXITY AND CHAOS
edited by Neal B. Abraham, Alfonso M. Albano,
Anthony Passamante, and Paul E. Rapp
Volume 225 - NONLINEAR EVOLUTION OF SPATIO-TEMPORAL STRUCTURES
IN DISSIPATIVE CONTINUOUS SYSTEMS
edited by F. H. Busse and L. Kramer
Volume 235 - DISORDER AND FRACTURE
edited by J. C. Charmet, S. Roux, and E. Guyon
Volume 236 - MICROSCOPIC SIMULATIONS OF COMPLEX FLOWS
edited by Michel Mareschal
Volume 240 - GLOBAL CLIMATE AND ECOSYSTEM CHANGE
edited by Gordon J. MacDonald and Luigi Sertorio
Volume 243 - DAVYDOV'S SOLITON REVISITED: Self-Trapping of Vibrational
Energy in Protein
edited by Peter L. Christiansen and Alwyn C. Scott
Volume 244 - NONLINEAR WAVE PROCESSES IN EXCITABLE MEDIA
edited by Arun V. Holden, Mario Markus, and Hans G. Othmer
Volume 245 - DIFFERENTIAL GEOMETRIC METHODS IN THEORETICAL
PHYSICS: Physics and Geometry
edited by Ling-Lie Chau and Werner Nahm
Volume 256 - INFORMATION DYNAMICS
edited by Harald Atmanspacher and Herbert Scheingraber
Volume 260 - SELF-ORGANIZATION, EMERGING PROPERTIES, AND
LEARNING
edited by Agnessa Babloyantz
Volume 263 - BIOLOGICALLY INSPIRED PHYSICS
edited by L. Peliti
Volume 264 - MICROSCOPIC ASPECTS OF NONLINEARITY IN CONDENSED
MATTER
edited by A. R. Bishop, V. L. Pokrovsky, and V. Tognetti
Volume 268 - THE GLOBAL GEOMETRY OF TURBULENCE: Impact of Nonlinear
Dynamics
edited by Javier Jimenez
SPECIAL PROGRAM ON CHAOS, ORDER, AND PATTERNS
Volume 270 - COMPLEXITY, CHAOS, AND BIOLOGICAL EVOLUTION
edited by Erik Mosekilde and Lis Mosekilde
Volume 272 - PREDICTABILITY, STABILITY, AND CHAOS IN N-BODY
DYNAMICAL SYSTEMS
edited by Archie E. Roy
Volume 276 - GROWTH AND FORM: Nonlinear Aspects
edited by M. Ben Amar, P. Pelce, and P. Tabeling
Volume 278 - PAINLEVE TRANSCENDENTS: Their Asymptotics and Physical
Applications
edited by Dacio Levi and Pavel Winternitz
Volume 280 - CHAOS, ORDER, AND PATTERNS
edited by Roberto Artuso, Predrag Cvitanovic, and Giulio Casati
Volume 284 - ASYMPTOTICS BEYOND ALL ORDERS
edited by Harvey Segur, Saleh Tanveer, and Herbert Levine
Volume 291 - PROTEIN TRANSFER IN HYDROGEN-BONDED SYSTEMS
edited by T. Bountis
Volume 292 - MICROSCOPIC SIMULATIONS OF COMPLEX HYDRODYNAMIC
PHENOMENA
edited by Michel Mareschal and Brad Lee Holian
Volume 298 - CHAOTIC DYNAMICS: Theory and Practice
edited by T. Bountis
Volume 312 - FUTURE DIRECTIONS OF NONLINEAR DYNAMICS IN PHYSICAL
AND BIOLOGICAL SYSTEMS
edited by P. L. Christiansen, J. C. Eilbeck, and R. D. Parmentier
Volume 320 - SINGULAR LIMITS OF DISPERSIVE WAVES
edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, and
D. Serre
Volume 323 - SOFT ORDER IN PHYSICAL SYSTEMS
edited by Y. Rabin and R. Bruinsma
Volume 329 - NONLINEAR COHERENT STRUCTURES IN PHYSICS
AND BIOLOGY
edited by K. H. Spatschek and F. G. Mertens
PREFACE
This volume contains the Proceedings of the NATO Advanced Research Workshop
(ARW) and Emil-Warburg-Symposium (EWS) "Nonlinear Coherent Structures in Phy
sics and Biology" held at the University of Bayreuth from June 1 - 4, 1993. Director
of the ARW was K. H. Spatschek, while F.G. Mertens acted as the co-director, host,
and organizer of the EWS. The other members of the scientific organizing committee
were A.R. Bishop (Los Alamos), J.C. Eilbeck (Edinburgh), and M. Remoissenet (Dijon).
This was the eighth meeting in a series of interdisciplinary workshops founded by our
French colleagues who had organized all the previous workshops, e.g. 1989 in Montpel
lier and 1991 in Dijon. We were asked to organize the meeting this time in Germany.
Of course, we wanted to keep the character defined by the previous meetings, which
were always characterized by an open and friendly atmosphere, being not too large
in quantity, but high in quality. This time altogether 103 participants attended the
workshop.
During the past years most of the participants met several times and discussed problems
connected with the generation of nonlinear coherent structures in physics and biology.
The interdisciplinary nature of such meetings, including researchers working on solid
state physics, fluid dynamics, nonlinear dynamics, biological physics, quantum physics,
etc. was always appreciated. It was agreed that the exchange of ideas among scientists
with different backgrounds is needed also in the future to develop this field. We are
now in the situation that there is a remarkable progress in understanding and model
ing nonlinear phenomena in various systems, and so in a stage of healthy growth the
workshop took place in Bayreuth.
The workshop covered areas from low-dimensional systems on the one end up to fully
developed turbulence on the other end. One of the central aspects was the role played
by solitons or solitary-wave-like structures in the nonlinear evolution of otherwise com
plicated infinite-dimensional systems. And here it turned out that during the last years
significant progress has been achieved experimentally, theoretically, and numerically by
various groups, and it was extremely important to communicate the new ideas and
methods between and beyond these groups in order to maintain and increase the know
ledge.
vii
The topics of interest were centered in the following areas:
I. Magnetic and optical systems;
II. Biosystems and molecular systems;
III. Josephson junctions and electrical transmission lines;
IV. Low-dimensional electronic materials;
V. Lattice dynamics and localized modes;
VI. Statistical mechanics and quantum mechanics of solitons;
VII. Multi-dimensional structures and pattern formation;
VIII. Numerical and analytical methods based on physical principles.
Many original contributions demonstrated that coherent structures, in the best known
cases solitons, play an important role in transport of both excitations and particles.
Another important result was the detection of localized modes and their consequences
for various physical and biological systems. And many more exciting new findings were
presented which can be found in the present Proceedings. We should emphasize that
each published manuscript went through a standard reviewing process, but despite of
that the responsibility for the contents lies, of course, with the authors.
We thank all participants for coming to Bayreuth, presenting their work, and con
tributing to a lively atmosphere during the meeting. Special thanks to the University
of Bayreuth, in particular to F. Gohmann, A. Neuper, H.J. Schnitzer and I. Fischer for
taking care of the local organisation. The assistance of E. Grc3ters and E. Ziigge during
the preparation of the Proceedings is also gratefully acknowledged. Last but not least
we thank NATO and the Emil-Warburg-Foundation for financial support. Without the
latter, many attendees, in particular from East Europe, would not have been able to
come, and this would have been a real loss.
October 1993
Franz G. Mertens Karl H. Spatschek
Universitii.t Bayreuth Heinrich-Heine Universitii.t Diisseldorf
Bayreuth, Germany Diisseldorf, Germany
viii
CONTENTS
SOLITONS ON LATTICES, LOCALIZED MODES, AND BIOPHYSICAL
APPLICATIONS
Quantum Lattices ............................................................ 1
J. C. Eilbeck and A. C. Scott
Recent Developments in the Quantum Nonlinear Dimer: Hopf Bifurcations,
Time Evolution, and Thermal Stability ............................... 15
V. M. Kenkre
Quantum Correlations of Toda Lattice ....................................... 19
A. Cuccoli, M. Spicci, V. Tognetti and R. Vaia
Energy Localization in Nonlinear Lattices .................................... 29
M. Peyrard, T. Dauxois and C. R. Willis
Anharmonic Localized Modes in Physical and Biological Systems .............. 39
S. Takeno
Soliton Scattering by an Impurity on a Nonlinear Lattice 51
S. Homma
Localized Excitations in Discrete Hamiltonian Systems........................ 59
S. Flach and C. R. Willis
Properties of Localized Excitations in Id Discrete Systems 63
S. Flach and C. R. Willis
Bound States in the Gaps of Periodic Lattices 67
J. Coste and J. Peyraud
Statistical Properties of Lattice Solitons 73
N. Theodorakopoulos
ix